"We want to deliver a unified message that killing the opposition is becoming more and more like a coup," Graham said.
The Obama administration has carefully avoided referring to the ouster of President Mohamed Morsi July 3 as a coup, which could force it to stop sending $1.5 billion in annual aid.
Senate Intelligence Committee Chairwoman Dianne Feinstein, D-Calif., said Sunday Congress should consider suspending the aid in response to an Egyptian security services attack Saturday that killed at least 72 people and wounded hundreds more.
Graham told CNN Tuesday the idea of the Egypt trip first came from Secretary of State John Kerry, who said it was important for military leaders to hear firsthand from U.S. lawmakers, especially members of Obama's political opposition, that key Washington players were on the same page.
He noted having McCain in Egypt on Obama's behalf could be especially symbolic, since McCain is Obama's former opponent for the White House.
"I think it really does demonstrate how democracy works. They didn't put John McCain in jail so he could never come back again," Graham said.